Yaadannoo boqonnaa fi gaaffii shaakalaa
Wanti fuula kana irra jiru hundi boqonnaa 8 kitaaba Herrega kutaa 11 tiif: wanta boqonnaan haguugu, yaadannoo gabaabaa, gaaffii shaakalaa deebii isaanii waliin, fi viidiyoo barnootaa bakka jirutti.
Gaaffii filannoo 10 boqonnaa kana irratti barreeffaman, tokkoon tokkoon isaanii deebii fi sababa qabu. Deebii banuu dura yaali. Gaaffiin kun Ingiliffaa tiin.
Gaaffii 1
A fair die is rolled once. How many outcomes are in the event of getting an odd number?
Deebii: B 3
Sababa
The event of getting an odd number is {1, 3, 5}. This event has 3 outcomes. The sample space {1, 2, 3, 4, 5, 6} has 6 outcomes, but the question asks only about the odd numbers.
Gaaffii 2
A fair coin is tossed three times. How many outcomes are in the sample space?
Deebii: C 8
Sababa
The textbook lists the sample space as HHH, HHT, HTH, THH, TTH, THT, HTT and TTT. That is 8 outcomes. Each toss has 2 results, so 2 x 2 x 2 = 8.
Gaaffii 3
A coin is tossed and a die is rolled at the same time. How many possible outcomes are there for this sequence of events?
Deebii: C 12
Sababa
A coin has 2 outcomes (H and T) and a die has 6 outcomes (1 to 6). By the multiplication principle, 2 x 6 = 12 possible outcomes.
Gaaffii 4
When a die is rolled, the event of getting an odd number is which type of event?
Deebii: B Compound event
Sababa
A simple event has only one sample element. A compound event has more than one. The event of getting an odd number is {1, 3, 5}, which has three elements, so it is a compound event.
Gaaffii 5
Tigist is choosing an outfit. She has 5 different pairs of pants, 4 different skirts and 12 different T-shirts. She wears either pants or a skirt, and always wears a T-shirt. How many outfits are possible?
Deebii: D 108
Sababa
Pants with a T-shirt give 5 x 12 = 60 outfits. Skirts with a T-shirt give 4 x 12 = 48 outfits. Because she cannot wear pants and a skirt together, we add: 60 + 48 = 108.
Gaaffii 6
In how many ways can five people be seated at a round table?
Deebii: B 24
Sababa
For circular arrangements, the number of permutations of n elements in a circle is (n - 1)!. Here n = 5, so (5 - 1)! = 4! = 4 x 3 x 2 x 1 = 24.
Gaaffii 7
Compute P(7, 4).
Deebii: C 840
Sababa
P(n, r) = n! / (n - r)!. So P(7, 4) = 7! / 3! = 7 x 6 x 5 x 4 = 840.
Gaaffii 8
Using Pascal's triangle, what is the coefficient of a2b2 in the expansion of (a + b)4?
Deebii: B 6
Sababa
The row for n = 4 in Pascal's triangle is 1, 4, 6, 4, 1. The expansion is a4 + 4a3b + 6a2b2 + 4ab3 + b4. The coefficient of a2b2 is 6.
Gaaffii 9
How many different permutations can be made from the letters of the word ADDIS if the arrangement must start with the letter S?
Deebii: A 12
Sababa
If S is fixed as the first letter, four letters remain: A, D, D and I. There are 2 D's, so the number of arrangements is 4! / 2! = 24 / 2 = 12. The textbook lists these 12 arrangements.
Gaaffii 10
In an HIV/AIDS club there are 7 women and 5 men. A committee of 3 women and 2 men is to be chosen. How many different committees are possible?
Deebii: D 350
Sababa
The 3 women can be chosen from 7 in C(7, 3) = 35 ways. The 2 men can be chosen from 5 in C(5, 2) = 10 ways. Because the women and men are chosen separately, we multiply: 35 x 10 = 350.
Appiin boqonnaa kana irratti gaaffii 12 qaba; utuu hojjettuu ni sirreessa. Kan asii jiran 10 jalqabaa ti.
Barnoota boqonnaa kanaa YouTube irraa. Yommuu play tuqxu qofa fe'ama.
Binomial Theorem (part 2) · YouTube irratti ilaali
Boqonnaan 8 Maxxansa Ministeera Barnootaa keessatti fuula 413 hanga fuula 482 ti.
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